A molten weld pool has two competing internal-flow drivers, drawn here as a vertical cross-section through the pool (the classic textbook view, rather than the top-down ring you'd see in a 3D render). Buoyancy convection is driven by gravity acting on the temperature-dependent density difference between the hot pool centre and cooler edges. Marangoni convection is driven by the temperature dependence of surface tension σ(T) — the free surface pulls toward whichever region has higher σ:
Buoyancy velocity scale: v_B ≈ √( g · β · ΔT · R )
Marangoni velocity scale: v_M ≈ |dσ/dT| · ΔT / μ
Grashof number: Gr = g · β · ΔT · R³ / ν²
Marangoni number: Ma = v_M · R / α
Regime: Gr/Ma ≫ 1 → buoyancy dominates (Earth)
Gr/Ma ≪ 1 → Marangoni dominates (orbit)
Numerically verified: at the default settings this ratio evaluates to ≈4.5 on Earth (buoyancy-dominated) and ≈0.014 in microgravity (Marangoni-dominated) — consistent with the physical picture below, so the ratio is carried over unchanged from the source model.
- Earth 1g / Microgravity — sets g in both scales. In orbit g ≈ 0, so Gr collapses to ~0 and buoyancy stops competing; the cross-section shows a single, symmetric pair of Marangoni recirculation rolls — exactly what electron-beam welding experiments on Salyut/Mir and the ISS were built to test.
- Sulfur / surfactant content — trace surface-active elements (S, O, Se) flip the sign of dσ/dT from negative (clean metal: hot centre has the lowest σ, surface flow spreads outward → shallow, wide pool, rolls turn "outward-at-surface") to positive above roughly 60–90 ppm (hot centre now has the highest σ, surface flow pulls inward and down → narrow, deep pool, rolls reverse to "inward-at-surface"). This sign flip is the real reason two "identical" welds on slightly different heats of steel can have very different penetration.
- Beam power — raises the peak surface temperature and hence ΔT across the pool, scaling both velocities and the pool radius R.
- Travel speed — elongates the pool into a comet-shaped trailing tail behind the beam; drag the cross-section left/right to follow the tail.
Particles in the cross-section trace the combined flow field: a pair of surface-hugging Marangoni rolls (direction set by the sulfur sign) plus, when gravity is on, a slower secondary buoyancy roll pair nested inside the pool that fights or reinforces it.